Finite Group Databasebeta

← #14676898

Subgroups — #14676898

Order 2816.

2474 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622833C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622563C211yesmaximal, characteristic, complemented
4C2×#10622824C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
6C22×C11⋊#95C211yesmaximal, characteristic, complemented
7#13066884C212yesmaximal, complemented
8#13066861C212yesmaximal, complemented
9#13066853C212yesmaximal, complemented
10#13066845C212yesmaximal, complemented
11C22×C11×#123C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C2×C11×#123—24no—
17C2×C11×#123—24no—
18C2×C11×#123C418yescomplemented
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×C4×Dic11C2212yes—
29#10622833—24no—
30#10622833—24no—
31#10622824—24no—
32C2×C11⋊#95—24no—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42#10622563—24no—
43C22⋊C4×Dic11—24no—
44C25×C11C2311yescharacteristic
45C25×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11C2×C414yes—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11C2×C414yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—24no—
67C23×Dic11—24no—
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—42no—
71C23×Dic11—42no—
72C23×Dic11D414yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2312yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2312yes—
78C23×Dic11C2311yescharacteristic
79C11×#123—232no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2×C418yescomplemented
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4C2×C414yes—
86C2×C11×C22⋊C4C2×C418yescomplemented
87C2×C11×C22⋊C4D414yes—
88C2×C11×C22⋊C4D414yes—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—42no—
100C2×C22⋊Dic11—42no—
101C2×C22⋊Dic11D414yes—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11—42no—
105C2×C4×Dic11—24no—
106C2×C4×Dic11—24no—
107C2×C4×Dic11—42no—
108C11⋊#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—22no—
116C11⋊#95—22no—
117#13996—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—21no—
125C24×C11—21no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—21no—
129C24×C11—21no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11C22×C412yes—
133C24×C11C22×C412yes—
134C24×C11C2×D412yes—
135C24×C11C2×D412yes—
136C24×C11C2×D412yes—
137C24×C11C2×D412yes—
138C24×C11#4112yes—
139C24×C11#4112yes—
140C24×C11C2411yescharacteristic
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—44no—
145C2×D4×C11—44no—
146C2×D4×C11—44no—
147C2×D4×C11—44no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—28no—
153C22×C4×C11—28no—
154C22×C4×C11—28no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—44no—
168C22×C4×C11—44no—
169C22×C4×C11—44no—
170C22×C4×C11—44no—
171C22×C4×C11C22×C414yes—
172C22×C4×C11C22×C412yes—
173C22×C4×C11C22×C414yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D414yes—
176C22×Dic11—28no—
177C22×Dic11—28no—
178C22×Dic11—28no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—21no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—44no—
209C22×Dic11—48no—
210C22×Dic11—48no—
211C22×Dic11—48no—
212C22×Dic11—48no—
213C22×Dic11—44no—
214C22×Dic11—44no—
215C22×Dic11C2×D414yes—
216C22×Dic11C2×D412yes—
217C22×Dic11C2×D412yes—
218C22×Dic11#4114yes—
219C22×Dic11#4114yes—
220C11×C4⋊C4—216no—
221C11×C22⋊C4—216no—
222C11×C22⋊C4C22⋊C4116yescomplemented
223C22⋊Dic11—28no—
224C22⋊Dic11—48no—
225C22⋊Dic11—44no—
226C22⋊Dic11—44no—
227C22⋊Dic11—44no—
228C4⋊Dic11—48no—
229C4×Dic11—48no—
230C22×#123D1111yescharacteristic
231C2×#386—111no—
232C2×#386—111no—
233C2×#385—111no—
234C2×#381—111no—
235C2×C4×C22⋊C4—111no—
236C22×#95—111no—
237#1445—112no—
238#1439—112no—
239#1437—112no—
240C4⋊#95—112no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—22no—
244C23×C11—22no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—24no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—42no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11C2×C22⋊C414yes—
281C23×C11C4×D414yes—
282C23×C11C4×D414yes—
283C23×C11#12114yes—
284C23×C11#12114yes—
285C23×C11#12414yes—
286C23×C11#12714yes—
287C23×C11C23×C411yescharacteristic
288C23×C11C22×D411yescharacteristic
289C23×C11C22×D411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11C2×#4111yescharacteristic
293C23×C11C2×#4111yescharacteristic
294C23×C11C2×#4112yes—
295C23×C11C2×#4112yes—
296C23×C11H(5,𝔽2)12yes—
297C23×C112−1+412yes—
298D4×C11—416no—
299C2×C4×C11—24no—
300C2×C4×C11—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—22no—
310C2×C4×C11—22no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—42no—
316C2×C4×C11—41no—
317C2×C4×C11—42no—
318C2×C4×C11—41no—
319C2×C4×C11—416no—
320C2×C4×C11C2×C22⋊C418yes—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—24no—
329C2×Dic11—22no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—416no—
335C2×Dic11—416no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C2×Dic11—42no—
343C2×Dic11—42no—
344C2×Dic11—42no—
345C2×Dic11—42no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11#12314yescomplemented
357C23×D4C2×D1111yescharacteristic
358C24×C4—111no—
359C24×C4—111no—
360C24×C4C2×D1111yescharacteristic
361C2×#123—24no—
362C2×#123—24no—
363C2×#123Dic1118yescomplemented
364C22×C4⋊C4—112no—
365C22×C4⋊C4C2×D1112yes—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4—112no—
370C22×C22⋊C4—111no—
371C22×C22⋊C4C2×D1112yes—
372C22×C22⋊C4C2×D1111yescharacteristic
373C22×C42—112no—
374#386—224no—
375#386—224no—
376#385—224no—
377#381—224no—
378C4×C22⋊C4—224no—
379C2×#95—111no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—111no—
388C2×#95—224no—
389C22×C11—24no—
390C22×C11—28no—
391C22×C11—28no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—28no—
395C22×C11—28no—
396C22×C11—24no—
397C22×C11—24no—
398C22×C11—24no—
399C22×C11—42no—
400C22×C11—44no—
401C22×C11—44no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—82no—
407C22×C11—82no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11#39018yes—
411C22×C11C22×C22⋊C411yescharacteristic
412C22×C11C2×C4×D411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C4×#4112yes—
415C22×C11#52012yes—
416C22×C11C2×#12111yescharacteristic
417C22×C11C2×#12111yescharacteristic
418C22×C11C2×#12311yescharacteristic
419C22×C11#52511yescharacteristic
420C22×C11C2×#12411yescharacteristic
421C22×C11#52912yes—
422C22×C11C2×#12711yescharacteristic
423C22×C11#53411yescharacteristic
424C22×C11#53611yescharacteristic
425C22×C11#53912yes—
426C22×C11#54612yes—
427C22×C11#54612yes—
428C22×C11#54612yes—
429C22×C11#54712yes—
430C22×C11#54712yes—
431C22×C11#54712yes—
432C22×C11#55112yes—
433C22×C11#55212yes—
434C4×C11—28no—
435C4×C11—44no—
436C4×C11—42no—
437Dic11—24no—
438Dic11—42no—
439Dic11—44no—
440Dic11—44no—
441Dic11—81no—
442Dic11—81no—
443C25C22×D1111yescharacteristic
444C25C22×D1111yescharacteristic
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4C2×Dic1114yes—
452C23×C4—22no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—22no—
458C23×C4—111no—
459C23×C4—112no—
460C23×C4—112no—
461C23×C4—111no—
462C23×C4—114no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—224no—
466C23×C4—224no—
467C23×C4—222no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—442no—
473C23×C4—442no—
474C23×C4C2×Dic1114yes—
475C23×C4C22×D1112yes—
476C23×C4C22×D1111yescharacteristic
477C23×C4C22×D1112yes—
478#123—232no—
479C2×C4⋊C4—24no—
480C2×C4⋊C4—24no—
481C2×C4⋊C4—224no—
482C2×C4⋊C4—224no—
483C2×C4⋊C4—442no—
484C2×C4⋊C4C2×Dic1118yescomplemented
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—114no—
488C2×C22⋊C4—222no—
489C2×C22⋊C4—222no—
490C2×C22⋊C4—222no—
491C2×C22⋊C4—224no—
492C2×C22⋊C4—222no—
493C2×C22⋊C4—224no—
494C2×C22⋊C4—224no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—442no—
499C2×C22⋊C4—442no—
500C2×C22⋊C4C2×Dic1114yes—
501C2×C22⋊C4C2×Dic1118yescomplemented
502C2×C22⋊C4C22⋊D1114yes—
503C2×C22⋊C4C22⋊D1114yes—
504C2×C42—224no—
505C2×C42—224no—
506C2×C42—442no—
507#95—224no—
508#95—224no—
509#95—224no—
510#95—224no—
511#95—222no—
512#95—224no—
513#95—222no—
514#95—224no—
515#95—224no—
516C2×C11—28no—
517C2×C11—82no—
518C2×C11C2×#39011yescharacteristic
519C2×C11C4×#12311yescharacteristic
520C2×C11#232211yescharacteristic
521C2×C11#233912yes—
522C2×C11#235912yes—
523C2×C11#241211yescharacteristic
524C2×C11#241311yescharacteristic
525C2×C11#242512yes—
526C2×C11#248812yes—
527C2×C11#250111yescharacteristic
528C2×C11#253911yescharacteristic
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—21no—
542C24—21no—
543C24D4×D1112yes—
544C24D4×D1112yes—
545C24#434112yes—
546C24#434112yes—
547C24C22×Dic1112yes—
548C24C22×Dic1112yes—
549C24C2×C22⋊D1112yes—
550C24C2×C22⋊D1112yes—
551C24C23×D1111yescharacteristic
552C2×D4—28no—
553C2×D4—28no—
554C2×D4—28no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—44no—
579C22×C4—44no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—112no—
583C22×C4—114no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—114no—
587C22×C4—228no—
588C22×C4—221no—
589C22×C4—222no—
590C22×C4—221no—
591C22×C4—228no—
592C22×C4—228no—
593C22×C4—222no—
594C22×C4—222no—
595C22×C4—222no—
596C22×C4—221no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—222no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—221no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—221no—
618C22×C4—221no—
619C22×C4—444no—
620C22×C4—448no—
621C22×C4—448no—
622C22×C4—448no—
623C22×C4—448no—
624C22×C4—444no—
625C22×C4—444no—
626C22×C4C22×Dic1114yes—
627C22×C4C22×Dic1112yes—
628C22×C4C22×Dic1114yes—
629C22×C4C2×C22⋊D1114yes—
630C22×C4C2×C22⋊D1114yes—
631C4⋊C4—216no—
632C4⋊C4—448no—
633C22⋊C4—216no—
634C22⋊C4—228no—
635C22⋊C4—444no—
636C22⋊C4—448no—
637C22⋊C4—444no—
638C22⋊C4—444no—
639C22⋊C4C22⋊Dic11116yescomplemented
640C42—448no—
641C11#1399611yescharacteristic, complemented, Sylow
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—24no—
651C23—22no—
652C23—22no—
653C23—24no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—22no—
659C23—22no—
660C23—24no—
661C23—24no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—41no—
676C23—42no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23D4×Dic1114yes—
682C23D4×Dic1114yes—
683C23#6698914yes—
684C23#6699114yes—
685C23#6699114yes—
686C23#6699314yes—
687C23C2×C22⋊Dic1114yes—
688C23C2×D4×D1111yescharacteristic
689C23C2×D4×D1111yescharacteristic
690C23C2×#434111yescharacteristic
691C23C2×#434111yescharacteristic
692C23#41×D1112yes—
693C23#41×D1112yes—
694C23#6704212yes—
695C23#6704312yes—
696C23C23×Dic1111yescharacteristic
697C23C22×C22⋊D1111yescharacteristic
698C23C22×C22⋊D1111yescharacteristic
699D4—416no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—416no—
721C2×C4—114no—
722C2×C4—222no—
723C2×C4—224no—
724C2×C4—222no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—222no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—4416no—
736C2×C4—4416no—
737C2×C4—442no—
738C2×C4—442no—
739C2×C4—442no—
740C2×C4—442no—
741C2×C4—442no—
742C2×C4—442no—
743C2×C4—442no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—442no—
750C2×C4—442no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—441no—
757C2×C4C2×C22⋊Dic1118yes—
758C22—24no—
759C22—28no—
760C22—28no—
761C22—28no—
762C22—24no—
763C22—24no—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—42no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—44no—
773C22—82no—
774C22—82no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22#1062283418yes—
780C22#1062317911yescharacteristic
781C22#1062318012yes—
782C22#1062318112yes—
783C22D11×#12311yescharacteristic
784C22#1062318411yescharacteristic
785C22#1062318512yes—
786C22#1062318612yes—
787C22#1062318711yescharacteristic
788C22#1062318912yes—
789C22#1062319612yes—
790C22C2×D4×Dic1111yescharacteristic
791C22C2×D4×Dic1111yescharacteristic
792C22C2×#6698911yescharacteristic
793C22C2×#6699111yescharacteristic
794C22C2×#6699111yescharacteristic
795C22C2×#6699311yescharacteristic
796C22#1062335512yes—
797C22#1062335512yes—
798C22#41×Dic1112yes—
799C22#1062335812yes—
800C22#1062336012yes—
801C22#1062336012yes—
802C22C22×C22⋊Dic1111yescharacteristic
803C4—28no—
804C4—44no—
805C4—42no—
806C4—224no—
807C4—444no—
808C4—442no—
809C4—444no—
810C4—881no—
811C4—881no—
812C2—28no—
813C2—82no—
814C2C2×#1062283411yescharacteristic
815C2#123×Dic1111yescharacteristic
816C2#1307128811yescharacteristic
817C2#1307144612yes—
818C2#1307161212yes—
819C2#1307200811yescharacteristic
820C2#1307201911yescharacteristic
821C2#1307216312yes—
822C2#1307294612yes—
823C2#1307308511yescharacteristic
824C2#1307354611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C11×#123C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×#123D11
hypocenterC11#13996
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#10622563C2semidirect
4. C2×#10622824C2semidirect
5. C2×C22⋊C4×Dic11C2semidirect
6. C22×C11⋊#95C2semidirect
7. #13066884C2semidirect
8. #13066861C2semidirect
9. #13066853C2semidirect
10. #13066845C2semidirect
18. C2×C11×#123C4semidirect
82. C2×C11×C4⋊C4C2×C4semidirect
86. C2×C11×C22⋊C4C2×C4semidirect
222. C11×C22⋊C4C22⋊C4semidirect
356. C2×Dic11#123semidirect
363. C2×#123Dic11semidirect
484. C2×C4⋊C4C2×Dic11semidirect
501. C2×C22⋊C4C2×Dic11semidirect
639. C22⋊C4C22⋊Dic11semidirect
641. C11#13996semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106228332
C2×#106225632
C2×#106228242
C2×C22⋊C4×Dic112
C22×C11⋊#952
#130668842
#130668612
#130668532
#130668452
C22×C11×#1232
#1399611